The aim of the study is the development of tools dedicated to fuzzy
partition evaluation in the field of satellite image classification.
While a traditional crisp partition only provides qualitative
information, a fuzzy partition represents a large amount of
quantitative information. However, such a partition is often evaluated
after “defuzzification”, i.e., it is reduced to a crisp partition. The
analysis of a traditional confusion matrix, describing the similarities
between the computed crisp partition and a control partition, can then
be performed. This approach is rather drastic and far from satisfactory
because the quantitative information is lost after the defuzzification.
Some methods do not require preliminary defuzzification, but they are
not adequate to evaluate nonprobabilistic fuzzy partitions (i.e.,
fuzzy partitions such that the sum of the membership degrees is not
necessarily equal to 1). To solve these issues, we consider the
evaluation of any fuzzy partition mu as the evaluation of a still fuzzy
new partition: the plausibilistic closure of mu. This approach comes
from the theory of evidence. It allows us to define a set of original
tools (plausibility matrices, credibility matrices, and overlap
degrees) dedicated to fuzzy partition evaluation. A concrete
application illustrates our theoretical work and a tutorial is provided
in appendix.
